基于SOS技术的多项式非线性系统鲁棒控制综合

黄文超; 孙洪飞; 曾建平

doi:10.3724/SP.J.1004.2013.00799

基于SOS技术的多项式非线性系统鲁棒控制综合

doi: 10.3724/SP.J.1004.2013.00799

1.
厦门大学自动化系厦门 361005

基金项目:

Supported by National Natural Science Foundation of China(61074004)

详细信息

通讯作者:
曾建平

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- 被引次数: 0
出版历程
- 收稿日期: 2012-01-10
- 修回日期: 2012-03-23
- 刊出日期: 2013-06-20

Robust Control Synthesis of Polynomial Nonlinear Systems Using Sum of Squares Technique

1.
Department of Automation, Xiamen University, Xiamen 361005, China

Funds:

Supported by National Natural Science Foundation of China(61074004)

摘要

摘要: 针对一类具有多项式向量场的仿射不确定非线性系统,借助多项式平方和(Sum of Squares, SOS)技术,研究其状态反馈鲁棒控制综合问题。给出了该类系统鲁棒镇定控制、以及带有保性能和H性能目标的优化控制问题的充分可解性条件。所给出的条件均被描述为由状态依赖线性矩阵不等式(LMI)组成的SOS规划,可由SOS技术直接求解。此外,通过引入附加变量给出了描述多项式矩阵的逆以及有理式矩阵的方法。最后,通过数值仿真验证了方法的有效性
- 非线性鲁棒控制 /
- 多项式系统 /
- 多项式平方和(SOS)
Abstract: In this paper, sum of squares (SOS) technique is used to analyze the robust state feedback synthesis problem for a class of uncertain affine nonlinear systems with polynomial vector fields. Sufficient conditions are given to obtain the solutions to the above control problem either without or with guaranteed cost or H performance objectives. Moreover, such solvable conditions can be formulated as SOS programming problems in terms of state dependent linear matrix inequalities (LMIs) which can be dealt with by the SOS technique directly. Besides, an idea is provided to describe the inverse of polynomial or even rational matrices by introducing some extra polynomials. A numerical example is presented to illustrate the effectiveness of the approach.
- Nonlinear /
- robust control /
- polynomial nonlinear systems

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参考文献(25)

[1]	Van der Schaft A J. L2-gain analysis of nonlinear systems and nonlinear state-feedback H∞ control. IEEE Transactions on Automatic Control, 1992, 37(6): 770-784
[2]	Isidori A, Astolfi A. Disturbance attenuation and H∞ control via measurement feedback in nonlinear systems. IEEE Transactions on Automatic Control, 1992, 37(9): 1283-1293
[3]	Isidori A. A necessary condition for nonlinear H∞ control via measurement feedback. Systems & Control Letters, 1994, 23(3): 169-177
[4]	Ball J A, Helton J W, Walker M L. H∞ control for nonlinear systems with output feedback. IEEE Transactions on Automatic Control, 1993, 38(4): 546-559
[5]	Lu W M, Doyle J C. H∞ control of nonlinear systems via output feedback: controller parameterization. IEEE Transactions on Automatic Control, 1994, 39(12): 2517-2521
[6]	Shen T L, Katsutoshi T. Robust H∞ control of uncertain nonlinear system via state feedback. IEEE Transactions on Automatic Control, 1995, 40(4): 766-768
[7]	Lu G P, Zheng Y F, Ho D W C. Nonlinear robust H∞ control via dynamic output feedback. Systems & Control Letters, 2000, 39(3): 193-202
[8]	Fu Y S, Tian Z H, Shi S J. Robust H∞ control of uncertain nonlinear systems. Automatica, 2006, 42(9): 1547-1552
[9]	Huang Y, Lu W M. Nonlinear optimal control: alternatives to Hamilton-Jacobi equation. In: Proceedings of the 1996 IEEE Conference on Decision and Control. Kobe, Japan: IEEE, 1996. 3942-3947
[10]	Huang Y. Nonlinear Optimal Control: An Enhanced Quasi-LPV Approach [Ph.D. dissertation], California Institute of Technology, USA, 1999
[11]	Freeman R A, Kokotovic P V. Optimal nonlinear controllers for feedback linearizable systems. In: Proceedings of the 1995 American Control Conference. Seattle, USA: IEEE, 1995. 2722-2726
[12]	Coutinho D, Trofino A, Fu M Y. Guaranteed cost control of uncertain nonlinear systems via polynomial Lyapunov functions. IEEE Transactions on Automatic Control, 2002, 47(9): 1575-1580
[13]	Prempain E. An application of the sum of squares decomposition to the L2-gain computation for a class of non linear systems. In: Proceedings of the 44th IEEE Conference on Decision and Control. Seville, Spain: IEEE, 2005. 6865-6868
[14]	Prajna S, Papachristodoulou A, Wu F. Nonlinear control synthesis by sum of squares optimization: a Lyapunov-based approach. In: Proceedings of the 5th Asian Control Conference. Melbourne, Australia: IEEE, 2004. 157-165
[15]	Zheng Q, Wu F. Nonlinear output feedback H∞ control for polynomial nonlinear systems. In: Proceedings of the 2008 American Control Conference. Seattle, USA: IEEE, 2008. 1196-1201
[16]	Xu J, Xie L H, Wang Y Y. Simultaneous stabilization and robust control of polynomial nonlinear systems using SOS techniques. IEEE Transactions on Automatic Control, 2009, 54(8): 1892-1897
[17]	Prajna S, Parrilo P A, Rantzer A. Nonlinear control synthesis by convex optimization. IEEE Transactions on Automatic Control, 2004, 49(2): 310-314
[18]	Hancock E J, Papachristodoulou A. Generalised absolute stability and sum of squares. In: Proceedings of the 2011 American Control Conference. San Francisco, USA: IEEE, 2011. 2302-2307
[19]	Tanaka K, Ohtake H, Seo T, Wang H O. An SOS-based observer design for polynomial fuzzy systems. In: Proceedings of the 2011 American Control Conference. San Francisco, USA: IEEE, 2011. 4953-4958
[20]	Mojica-Nava E, Quijano N, Rakoto-Ravalontsalama N, Gauthier A. A polynomial approach for stability analysis of switched systems. Systems & Control Letters, 2010, 59(2): 98-104
[21]	Parrilo P A, Sturmfels B. Minimizing polynomial functions. In: DIMACS Series in Discrete Mathematics and Theoretical Computer Science. Rutgers University: DIMACS, 2001, 60: 83-99
[22]	Reznick B. Some concrete aspects of Hilbert's 17m th problem. Contemporary Mathematics, 2000, 253: 251-272
[23]	Nguang S K. Robust nonlinear H∞ output feedback control. IEEE Transactions on Automatic Control, 1996, 41(7): 1003-1007
[24]	Yu L. Robust Control——Linear Matrix Inequality Approach. Beijing: Tsinghua University Press, 2002. 88-89
[25]	Zhou K M, Doyle J C, Glover K. Robust and Optimal Control. New Jersey: Prentice Hall, 1996. 367-373